math.ST · 2026-08-15 · No. 85

Statistics Theory, 2026-08-15.

2 new papers in math.ST. Titles, authors, abstracts. Links to arXiv. Want this in your inbox every morning? Subscribe →

01 — The papers

2 entries
  1. 01

    On the Structural Limits of Machine Learning Decision Systems: An Information-Theoretic, Interaction-Based, and Stochastic-Dynamical Perspective

    Nestor R. Barraza, Gabriel Pena

    math.ST · cs.LG

    Machine learning procedures are commonly evaluated in terms of predictive accuracy and computational efficiency. However, their achievable performance is fundamentally constrained by structural properties of the underlying data-generating process, which are formalized in terms of informational bounds. In this work we examine intrinsic limits of data-driven decision systems from an information-theoretic and interaction-based perspective. We...

    arxiv.org/abs/2608.13510 · PDF

  2. 02

    Foundations of Independent Component Analysis

    Patrick Forré

    math.ST · cs.LG · math.PR · stat.ML

    We present the mathematical foundations of linear independent component analysis (ICA) models based on standard literature in a self-contained note. It is aimed at readers with a background in measure-theoretic probability theory. We first develop the theory of the characteristic functions of probability measures on $\mathbb{R}^d$, including their analyticity and the way in which they determine and characterise the distributions. We then...

    arxiv.org/abs/2608.13229 · PDF

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